Unformatted text preview: T : V → V be lienar. Prove that T 2 = T if and only if R ( T ) ⊆ N ( T ), where T is the zero transformation, i.e. T ( v ) = 0 for all v ∈ V , and T 2 := T ◦ T is the composition of T and T , i.e. T 2 ( v ) := T ( T ( v )) for all v ∈ V . ( Note : It is a “twoway” statement, you need to prove both directions, i.e prove “= ⇒ ” as well as “ ⇐ =”). 7. Problem 2(a), (e) (f) on Page 106 1...
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 Summer '08
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 Linear Algebra, Algebra, Vector Space, Linear map, advanced linear algebra

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